Geometry 2 polygons
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Mathematics Geometry Grade 10
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Geometry 2 polygons
- 2. Polygons Quadrilaterals Sufficient conditions Polygons Polygons Sum of the interior angles of a polygon with n sides = (n – 2)180º Sum of the exterioranglesof any polygon = 360º A regular polygon is a polygon with equal sidesand therefore equal anglestoo. Every interior angle of a regular polygon with nsides 360o n . Polygons . Important formulas concerning polygons: n Every exterior angle of a regular polygon with nsides = 2 o = (n 2)180
- 3. Names ofpolygons Triangle (3sides) Quadrilateral(4sides) Pentagon(5sides) Hexagon(6sides) Heptagon(7sides) Octagon (8sides) Nonagon(9sides) Decagon (10sides) Example Find the size of the angles indicated by letters: FlashCard Quadrilateral 4 sides, 4 angles FlashCard Quadrilateral (4) A Quad Bike has 4 wheels FlashCard 3
- 4. FlashCard pentagon 5 sides, 5 angles FlashCard FlashCard pentagon 5 sides, 5 angles Buckyball: 12 pentagons (see black patches), 20 hexagons FlashCard Hexagon 6 sides, 6 angles FlashCard heXagon 6 sides, 6angles FlashCard 4 Think X: siX
- 5. FlashCard hexagon 6 sides, 6angles Buckyball: 12 pentagons, 20 hexagons (see white patches) FlashCard heptagon 7 sides, 7 angles FlashCard heptagon 7 sides, 7angles FlashCard FlashCard octagon 8 sides, 8 angles FlashCard 5
- 6. octagon think octopus FlashCard octagon 8 sides, 8angles FlashCard 4 Special Quadrilaterals •TheParallelogram A four-sided polygon with two pairs ofparallel and equal sides. •Rectangle: A rectangle is a parallelogram with rightangles. • Square: A square is a rectangle with 4 equalsides. •Rhombus: A rhombus is a parallelogram with 4 equal sides. Special Quadrilaterals • Trapezium: A trapezium is a quadrilateral with only one pairof parallel sides • Kite: A quadrilateral in which two pairs of adjacent sides are equal The familytree 6
- 7. SpecialQuadrilaterals:properties Example Find the values of x andy. Given: AD║BC Find the values of x andy. Exercise Findx Parallelogram Sufficient conditions to provea parallelogram Prove one of the following: • Both pairs of opposite sides parallel • Both pairs of opposite sides equal • Both pairs of opposite angles equal • Diagonals bisect each other • One pair of opposite sides parallel and equal 7
- 8. Rectangle Sufficient conditions to provea rectangle • Prove the quadrilateral is a parallelogram AND one interior angle equals 𝟗𝟎° Rhombus Sufficient conditions to provea rhombus • Prove the quadrilateral is a parallelogram AND one pair of adjacent sides are equal Square Sufficient conditions to provea square • Prove the quadrilateral is a parallelogram AND one interior angle equals 𝟗𝟎° AND one pair of adjacent sides is equal 8
- 9. Kite Sufficient conditions to provea kite •Prove that two pairs of adjacent sides are equal • Remember: NOT a parallelogram Trapezium Sufficient conditions to provea trapezium •Prove that one pair of opposite sides are parallel • Remember: NOT a parallelogram Example: ABCD is a parallelogram with DF = EB. Prove that AECF is a parallelogram. Complete the following statements: 9 2. 3. 4. 5. 1 If the diagonals of a quadrilateral are not equal, but bisect each other perpendicularly, the quadrilateral is a……… A triangle that has three equal sides is called an ….… triangle. If both pairs of adjacent sides of a quadrilateral are equal, but the opposite sides are not equal, the quadrilateral is a ……. If the diagonals of a quadrilateral are equal and bisect each other perpendicularly, the quadrilateral is a….… If both pairs of opposite angles of a quadrilateral are equal, the quadrilateral is a ……